A vehicle starts moving along a straight line path from rest. In first `t` seconds it moves with an acceleration of 2 m/s² and then in next 10 seconds it moves with an acceleration of 5 m/s². The total distance travelled by the vehicle is 550 m. The value of time `t` is
10 s
13 s
20 s
25 s
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC NDA-2 – 2024
For the second phase (t to t+10 seconds): Initial velocity (u₂) = v₁ = 2t m/s, acceleration (a₂) = 5 m/s², time (t₂) = 10 s. Distance s₂ = u₂t₂ + (1/2)a₂t₂² = (2t)*10 + (1/2)*5*(10)² = 20t + 250 m.
Total distance = s₁ + s₂ = t² + 20t + 250. Given total distance is 550 m, t² + 20t + 250 = 550, which simplifies to t² + 20t – 300 = 0.
Factoring the quadratic: (t + 30)(t – 10) = 0. Possible solutions are t = -30 or t = 10. Since time cannot be negative, t = 10 s.